A Bayesian Approach for the Estimation of the Particle Size Distribution Combining Static Light Scattering and Scaning Electron Microscopy

FERNANDO OTERO; GLORIA FRONTINI; GUILLERMO E. ELICABE

Albi

Simposio; 4th Inverse Problems, Design and Optimization Symposium (IPDO-2013); 2013

IPDO SOCIETY

In this article, Static Light Scattering (SLS) measurements are processed to estimate the Particle Size Distribution (PSD) of polymeric particle systems incorporating prior information obtained from an alternative experimental technique: Scanning Electron Microscopy (SEM). SEM is a direct experimental technique for particle sizing but it uses just a small fraction of the particles so it has a considerable statistical error. The resulting inverse problem is solved using a Bayesian approach, implemented through the Metropolis- Hastings (MH) algorithm, following two different schemes for the representation of the PSD. In the first one, the PSD is represented by a parameterized family of distributions in a fixed-form scheme. In the second one, there is no assumption on the shape of the PSD, i.e. a free-form scheme is used. Both schemes are tested by analysis of simulated examples of concentrate and semi-concentrate polymeric particles where simulated SLS measurements are generated using a rigurous model (Vrij?s Hard Sphere (HS) model) while an approximate model (Pedersen?s Local Monodisperse Approximation (LMA)) is used in the inversion stage. A few priors from SEM micrographs are simulated in a Monte Carlo routine. Results show that a Bayesian approach combining data from two experimental techniques is recommended when using an approximate model and reliable additional information can be made use of.